On stable refinable function vectors with arbitrary support

Authors:
Sandra Saliani
Affiliations:
Dipartimento di Matematica e Informatica, Universití degli Studi della Basilicata, 85100 Potenza, Italie
Venue:
Journal of Approximation Theory
Year:
2008

Citing 6
Cited 0

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Abstract

Refinable function vectors with arbitrary support are considered. In particular, necessary conditions for stability are given and a characterization of the symbol associated with a stable refinable function vector in terms of the transfer operator is provided: this is a generalization of Gundy's theorem to the vector case. The proof adapts the tools provided in [S. Saliani, On stability and orthogonality of refinable functions, Appl. Comput. Harmon. Anal. 21 (2006) 254-261]. Though complications arise from noncommuting matrix products, the fundamental ideas are the same.